A new approach to computing the Euler characteristic

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摘要

In this paper we describe a new approach to computing the Euler characteristic of a three dimensional digital image. Our approach is based on computing the change in numbers of black components, tunnels and cavities in 3 × 3 × 3 neighborhood of an object (black) point due to its deletion. The existing algorithms to computing the Euler characteristic of a 3D digital image are based on counting the numbers of all k-dimensional elements (0 ≤ k ≤ 3) in a polyhedral representation of the image. Our approach can be modified for (6,26), (18,6), (6,18) and other connectivity relations of grid points. A parallel implementation of the algorithm is described using the concept of sub-fields.

论文关键词:3D digital topology,Betti numbers,Tunnels,Binary transformation,Euler characteristic,Sub-fields

论文评审过程:Received 23 March 1995, Revised 7 April 1995, Available online 7 June 2001.

论文官网地址:https://doi.org/10.1016/0031-3203(95)00058-5